The field of endeavor of the present embodiments is generally illumination optics, and more specifically the design of lenses and other luminaires that are generally not rotationally symmetric
Some optical problems are stated in two-dimensional (2D) geometry and solved with particular line profiles by which solution-surfaces can be generated by means of a circular or linear sweep. Deviations from circular symmetry are generally treated as troublesome aberrations, as for example astigmatism of a tilted input wavefront.
Optical free-form surfaces are figures of burgeoning interest, because of both theoretical advances in their mathematical description and technological advances in their cost-effective manufacture. With the advent of injection molding of plastic optics, mass-replication of free-form surfaces becomes possible. The development of electrical-discharge machining (EDM) has provided means for fabricating optical-quality freeform surfaces in the metal of the mold. EDM in turn depends upon five-axis and six-axis machining to produce the desired free-form surface as a carbon electrode of identical dimensions as the part to be produced. This electrode is used to electrically burn into metal a concavity matching its own shape, thereby providing a mold cavity that imparts the desired shape to molten plastic. Beyond the replicative methods of injection molding, free-form surfaces can be produced directly in some optical materials, such as acrylic, with multi-axis machining techniques, albeit at greater per-part expense than injection molding and thus typically employed for prototypes.
Two important applications of free-form optical surfaces for illumination are conformal optics and asymmetric output. Conformal optics refers to systems with an arbitrary shape that is dictated by aerodynamics, hydrodynamics, and/or other such non-optical criteria, e.g. shapes that must conform to that of a vehicle's exterior surface. Asymmetric output arises when a system's illumination requirements are not rotationally symmetric, so that the traditional rotational symmetry of some illumination optics are generally inadequate. The additional degree of freedom of non-symmetry calls for an expanded, more general method of surface synthesis than the generation of a planar profile for sweeping into a surface.